Light - Reflection and Refraction — Study Notes

1. Introduction

Light is a form of energy that enables us to see the world around us. It travels in straight lines and can be reflected, refracted, absorbed and scattered. The study of light begins with two fundamental phenomena: reflection, where light bounces back from a surface, and refraction, where light bends while passing from one transparent medium to another. These phenomena govern the working of mirrors, lenses, optical instruments and even our own eyes.

A ray of light is the path along which light travels, and a collection of rays is called a beam of light. When light falls on a smooth, polished surface, it is reflected back according to well-defined laws. When it passes from one medium to another, such as from air to glass or water, it changes speed and direction. Both reflection and refraction are used extensively in daily life, from the mirrors in vehicles to the lenses in spectacles, cameras and telescopes.

In this chapter, we will study the laws of reflection, image formation by plane and spherical mirrors, the mirror formula and magnification, the laws of refraction, refractive index, image formation by lenses, the lens formula, and the power of a lens. Numerical problems based on the mirror formula (1/v + 1/u = 1/f) and the lens formula (1/v - 1/u = 1/f) are a key part of the examination.

2. Reflection of Light and Plane Mirrors

Laws of Reflection

When a ray of light strikes a reflecting surface:

1. The angle of incidence is equal to the angle of reflection (i = r).
2. The incident ray, the reflected ray and the normal, all lie in the same plane.

Image Formation by a Plane Mirror

A plane mirror forms an image which is:

• Virtual and erect.
• Same size as the object.
• At the same distance behind the mirror as the object is in front.
• Laterally inverted (left appears as right).

The image formed by a plane mirror cannot be obtained on a screen, so it is called a virtual image.

3. Spherical Mirrors

A spherical mirror is a mirror whose reflecting surface is a part of a hollow sphere. It is of two types:

• Concave mirror: the reflecting surface is curved inwards. It converges light rays.
• Convex mirror: the reflecting surface is curved outwards. It diverges light rays.

Key Terms

• Pole (P): the centre of the reflecting surface.
• Centre of curvature (C): the centre of the hollow sphere of which the mirror is a part.
• Radius of curvature (R): the distance between P and C, so R = 2f.
• Focus (F): the point where rays parallel to the principal axis converge (concave) or appear to diverge from (convex).
• Focal length (f): the distance between P and F.

$$f = \frac{R}{2}$$

Rules for Drawing Ray Diagrams

1. A ray parallel to the principal axis passes through the focus (or appears to come from the focus).
2. A ray passing through the focus becomes parallel to the principal axis after reflection.
3. A ray passing through the centre of curvature retraces its path after reflection.
4. A ray incident at the pole reflects back making an equal angle with the principal axis.

Image Formation by a Concave Mirror

The image formed by a concave mirror depends on the position of the object:

Uses of Concave and Convex Mirrors

Concave mirrors are used in shaving mirrors, torch reflectors, headlights of vehicles and solar cookers, because they converge light. Convex mirrors are used as rear-view mirrors in vehicles because they give a wider field of view and always form erect, diminished images.

4. The Mirror Formula and Magnification

The mirror formula relates the object distance (u), image distance (v) and focal length (f):

$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$

The sign convention used is the Cartesian sign convention: all distances are measured from the pole, distances in the direction of incident light are positive, and distances opposite to the direction of incident light are negative. For a concave mirror, f is negative; for a convex mirror, f is positive.

Magnification (m) is the ratio of the height of the image (h') to the height of the object (h):

$$m = \frac{h'}{h} = -\frac{v}{u}$$

A negative magnification indicates a real, inverted image, while a positive magnification indicates a virtual, erect image.

5. Refraction of Light

Refraction is the bending of light when it passes obliquely from one transparent medium to another, because the speed of light changes. When light travels from a rarer medium (like air) to a denser medium (like glass or water), it bends towards the normal. When it travels from a denser to a rarer medium, it bends away from the normal.

Laws of Refraction

1. The incident ray, the refracted ray and the normal all lie in the same plane.
2. Snell's law: the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.

$$\frac{\sin i}{\sin r} = \text{constant}$$

Refractive Index

The refractive index (n) of a medium is the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v):

$$n = \frac{c}{v}$$

The relative refractive index of medium 2 with respect to medium 1 is:

$$n_{21} = \frac{v_1}{v_2}$$

Refraction Through a Glass Slab and Prism

When light passes through a rectangular glass slab, it emerges parallel to the incident ray but laterally displaced. The emergent ray is parallel to the incident ray because the refraction at the two parallel surfaces is equal and opposite.

6. Lenses

A lens is a transparent material bounded by two surfaces, of which at least one is curved. Lenses are of two types:

• Convex (converging) lens: thicker at the centre than at the edges; converges light rays.
• Concave (diverging) lens: thinner at the centre than at the edges; diverges light rays.

Key Terms for Lenses

• Optical centre (O): the centre of the lens.
• Principal focus (F): the point where rays parallel to the principal axis converge (convex) or appear to diverge from (concave).
• Focal length (f): the distance between the optical centre and the focus.

Image Formation by a Convex Lens

A convex lens is used as a magnifying glass, in cameras, projectors, spectacles for hypermetropia, and in the human eye. A concave lens is used in spectacles for myopia and in some optical instruments.

The Lens Formula and Power of a Lens

The lens formula relates u, v and f:

$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$

The power of a lens is the reciprocal of its focal length in metres:

$$P = \frac{1}{f \text{ (in m)}}$$

The SI unit of power is the dioptre (D). The power of a convex lens is positive, and the power of a concave lens is negative.

Quick Revision Tables

Table 1: Sign Conventions for Mirrors and Lenses

Table 2: Differences between Reflection and Refraction

Mind Map

Important Diagrams (SVG)

Diagram 1: Image Formation by a Concave Mirror (Object between F and C)

Diagram 2: Refraction Through a Glass Slab

Common Mistakes

1. Writing the mirror formula as 1/v - 1/u = 1/f; the mirror formula is 1/v + 1/u = 1/f, while the lens formula is 1/v - 1/u = 1/f.
2. Ignoring the sign convention; object distance (u) is always negative for both mirrors and lenses.
3. Confusing the focal length sign: concave mirror f is negative, convex mirror f is positive, convex lens f is positive, concave lens f is negative.
4. Saying the convex mirror forms a real image; a convex mirror always forms a virtual, erect and diminished image.
5. Believing that the image formed by a plane mirror is real; it is virtual, erect, same size and laterally inverted.
6. Forgetting that power is measured in dioptres only when the focal length is in metres, and that convex lens power is positive while concave lens power is negative.
7. Mixing up the refraction direction: light bends towards the normal when going from rarer to denser, not away from it.

Exam Tips

1. Memorise both formulae exactly: mirror formula 1/v + 1/u = 1/f and lens formula 1/v - 1/u = 1/f.
2. Apply the Cartesian sign convention systematically: u is always negative, v is positive for real images and negative for virtual images.
3. Learn the position-nature table for concave mirrors and convex lenses, as "position of object vs nature of image" questions are common.
4. Know the uses: concave mirror (shaving, torch, solar cooker), convex mirror (rear-view mirror), convex lens (magnifying glass, camera, hypermetropia), concave lens (myopia).
5. For magnification, remember m = -v/u and interpret the sign: negative means inverted, positive means erect.
6. In refraction, remember n = c/v and that the refractive index of a medium is always greater than 1 relative to vacuum.
7. Practise at least three numericals on the mirror formula and three on the lens formula, including power calculations.

Conclusion

Light, with its phenomena of reflection and refraction, is fundamental to vision and to countless optical devices. The laws of reflection and refraction, though simple to state, give rise to the rich behaviour of mirrors and lenses that is applied everywhere, from car rear-view mirrors to the human eye. Spherical mirrors and lenses obey precise mathematical relationships, summarised in the mirror and lens formulae, which allow us to predict the position, nature and size of images. The sign convention and the concept of magnification turn these formulae into practical problem-solving tools. Refraction explains the working of glass slabs, prisms, lenses and optical instruments. A mastery of ray diagrams, the key formulae and their applications will ensure both good scores in the examination and a deeper appreciation of the optics that surrounds our daily lives.